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Last Time: Linear Momentum & Impulse
vmp
• Linear momentum of an object is mass times velocity
• Linear momentum is a vector. Direction of linear
momentum is the same as the velocity of the object
Units: kg m/s
tFpI
1. A force must act on an object for impulse to occur
2. In a collision, an impulse occurs in the direction of
the force acting on the object
t
pFnet
Main Ideas in Class Today
After today’s class, you should be able to:
• Understand what a “system” is and
determine whether it is isolated
• Apply Conservation of Linear
Momentum to determine a final velocity
in one or two dimensions
Extra Practice: 6.21, 6.23, 6.27, 6.65
What is a System?
2112, FFF systemnet
2112 FF
0, systemnetF
A system is a set of objects interacting with each other
(set of pool balls, ball/bat, students in this room)
An isolated system has no unbalanced external forces, meaning no unbalanced forces outside the system (e.g., normal/gravity)
In an isolated system Fnet,system=0
because of Newton’s Third Law:
Isolated System?Ignore air resistance.
Cars crashing on ice
(ignore friction, small)
Two boats crashing
Jumping guy hits soccer ball in air Q70-72
A.Yes.
B.No.
Car and Zombie moving
with constant velocity
(before and after hitting
each other)
Why did
car’s/zombie’s
velocity matter?
Isolated System?
A.Yes.
B.No. Q73-74
Car and Tree
Even if a system isn’t isolated,
sometimes we can approximate it as
isolated by only considering just before
and after the instant of the collision(other forces don’t have much time to act)
Would not work here (external force has a large
impact on the result)Would work fine
There is Conservation of Linear
Momentum in Isolated Systems.
N’s 2nd Law:
0,
t
pF
system
systemnet
0,, systemisystemfsystem ppp
systemisystemf pp ,,
Ex: collision of two billiard
balls on a frictionless surface
ffii vmvmvmvm 22112211
0, systemnetF
This is a vector formula.
What does that mean?
Initial (i)
Final (f’)
fvm 11
fvm 22
While not isolated in
the y direction, can
use momentum
formula in x
direction.
Recoil
A rifle with a weight (W=mg) of 20 N fires a
4.0 g bullet with a speed of 280 m/s.
(a) Find the recoil speed of the rifle.
(b) If a 725 N man holds the rifle firmly
against his shoulder, find the recoil speed of
the man and rifle.
What is the system?
How do we know this is a momentum problem?
Conservation of momentum
The head of a 0.2 kg golf club is
traveling at 55 m/s just before it
strikes a 0.046 kg golf ball at rest on
a tee. After the collision, the club
head travels (in the same direction)
at 40 m/s. Find the speed of the golf
ball just after impact.
Treat the system as isolated during
the instant of collision.
Colliding objects
• Let m2=2m1, so m2 is twice as massive.
• Let’s say you hit ball 1 with v1i=10m/s into
stationary ball 2, v2i= 0 m/s.
• Let’s say that after the collision, ball 1 is
stationary. (not always the case)
• What is the final velocity of ball 2?
A) 5 m/s
B) 10 m/s
C) 20 m/s
D) -5 m/s
E) -20 m/s
initial finalm2=2m1
m2
Q75
m1
An open cart is rolling to the
left at a constant speed on a
horizontal surface. A package
slides down a chute and lands
in the cart. Which quantities
have the same value just
before and just after the
package lands in the cart?
A. The horizontal component of total momentum
B. The vertical component of total momentum
C. Both of the above
D. None of the above Q76
A 500-kg freight package is dropped
vertically onto a 1000-kg rail cart
moving at 6 m/s. The package is moving
at 3 m/s just before landing on the cart.
After the drop, the speed of the cart and
package is closest to:
A. 9 m/s
B. 7 m/s
C. 6 m/s
D. 4 m/s
E. 3 m/s Q77
vi = 6 m/s
Example: A Runaway Railroad CarA 14,000 kg railroad car is rolling at
4.00 m/s toward an intersection. As it passes a grain elevator, 2,000 kg of grain suddenly drops vertically into the car. Ignore friction and air drag.
How long does it take for the car to travel the 500 m distance from the grain elevator to the intersection?
sys
i ext g grain g car n
PF F F F
t
sys fx sys ixP P ( ) (0)c g f x c ix gm m v m v m c
f x ix
c g
mv v
m m
( ) (500 m)(14000 kg 2000 kg)143 s
(14000 kg)(4.00 m/s)
c g
fx
c ix
d m md v t t
m v
Conserved in x direction
An astronaut in her space suit has a total mass of m1 = 87
kg, including her oxygen tank. Her tether line loses its
attachment to her spacecraft and she is too far to grab on!
Initially at rest with respect to her spacecraft, she throws
her oxygen tank of mass m2 = 12.0-kg away from her
spacecraft with a speed v = 8.00 m/s to propel herself back
toward the spacecraft.
Determine the maximum distance she can be from the
craft and still return within 2.00 min (the amount of time
the air in her helmet remains breathable).
Forces of Motion
• Cars move due to the force of friction
between the tires and road.
• Planes take advantage of air resistance.
• Boats use the resistance of the water.
• But what about rockets in space?
There is no air in space to provide a
resistance
The New York Times Response
To Rockets in Space("New York Times," 13 January, 1920, p. 12, col. 5)
“That Professor Goddard…does not know the
relation of action to reaction, and … the need
to have something better than a vacuum
against which to react--to say that would be
absurd. Of course he only seems to lack the
knowledge ladled out daily in high schools.”
What do you think about this critique?
2 Lessons: Even brilliant scientists make mistakes.
And frequently, even experts don’t agree.
Diet Coke and Mentos
www.youtube.com/watch?v=22cfLVtUWn8
What does
this have to
do with
rockets?
Rocket Propulsion
• While it’s true that there is no friction to
propel rockets forward in space, there is
conservation of momentum.
systemfsystemi pp ,,
22112211 vmvmvmvm ii
Instead of throwing the
tank, imagine just letting the
gas in the tank spray out
(safer, but slower)
Note: Changing mass
Let’s consider this situation again
Could find recoil of soccer player.
Cardiology
(Challenging setup)
In research of cardiology and exercise physiology, it is often important
to know the mass of blood pumped by a person's heart in one stroke.
This information can be obtained by means of a ballistocardiograph.
The instrument works as follows: The subject lies on a horizontal pallet
floating on a film of air. Friction on the pallet is negligible. Initially, the
momentum of the system is zero. When the heart beats, it expels a mass
m of blood into the aorta with speed v, and the body and platform move
in the opposite direction with speed V. The speed of the blood can be
determined independently. Assume that the blood's speed is 50.0 cm/s in
one typical trial. The mass of the subject plus the pallet is 54.0 kg. The
pallet moves 6.00 10-5 m in 0.160 s after one heartbeat. Calculate the
mass of blood that leaves the heart. Assume that the mass of blood is
negligible compared with the total mass of the person.
Chapter/Section: Clicker #=Answer
Ch.6: 67=B, 68=A, 69=B
Ch.6B: 70=B, 71=A, 72=B, 73=A, 74=B, 75=A, 76=A,
77=D
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